Please help with the following problems, and please use matlab for part c. Thank you.

A device parameter X is a continuous random variable that takes values over [1,1] and is uniform over that interval. We take a measurement Y ,oX3 + N where p % 0 is a given parameter and NN ~,N(0 02) is independent noise. Dene X1(Y) aY as the linear MMSE estimator (for an optimized (1). Dene X3(Y): E [X|Y]. Assume p 0 7 and observe that Y now depends on X3 rather than X. a) Compute the optimal a and the corresponding MSE for estimator X1[Y} = aY, the best linear estimator. b) Compute X3 (y) 2 E [X |Y = y] in terms of an integral. The numerator of the integral cannot be solved in closed form. c) Write a program that, for values 02 6 [0.0001, 0.1] does the following: Given 02, run so : 1000 samples to generate i.i.d. (X13, 1;) values. Take the empirical values MSElemprm; = %2321(X1(1) Xi)? Plot as a function of a2 and compare with the theoretical value for MSE in part (a), also compare with the constant Var-(X) which is the MSE obtained by the best constant estimator, and with MSE3emprim; 171321(X3(Y') .You can use the matlab integral command if you like (a sample will be given on Piazza). Your MSE3 should always be )at least as good as MSE], but should be a little better when 02 is small